Order types and cross-sections of line arrangements in ℝ3

Oswin Aichholzer, Ruy Fabila-Monroy, Ferran Hurtado, Pablo Pérez-Lantero, Andres J. Ruiz-Vargas, Jorge Urrutia, Birgit Vogtenhuber

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


We consider sets 葦 = {ℓ1;.,ℓn} of n labeled lines in general position in ℝ3, and study the order types of point sets {p1;.; pn} that stem from the intersections of the lines in L with (directed) planes II not parallel to any line of 葦, i.e., the proper cross-sections of 葦. As a main result we show that the number of diérent order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight.

Original languageEnglish
Title of host publication26th Canadian Conference on Computational Geometry, CCCG 2014
PublisherCanadian Conference on Computational Geometry
Number of pages6
Publication statusPublished - 2014
Event26th Canadian Conference on Computational Geometry: CCCG 2014 - Halifax, Canada
Duration: 11 Aug 201413 Aug 2014


Conference26th Canadian Conference on Computational Geometry

ASJC Scopus subject areas

  • Geometry and Topology
  • Computational Mathematics


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